IntroductionPrinciples of Nuclear Energy*

Bohrs ModelU23592EXAMPLENuclear Energy (Basics: Atomic Structure)Z = atomic numbernumber of protons in an atom

N = number of neutrons

A = Z + N = mass numbernumber of protons plus number of neutrons*

Two nuclei with the same number of protons can have different number of neutrons and are calledisotopes of the same element.Example:isotopes+++Nuclear Energy (Basics: Atomic Structure)HYDROGENDEUTERIUMTRITIUM:*

Atomic Mass Unit is a unit of mass equal to 1.66x10-27 kg.Proton(+1)1.007277 amuNeutron(0)1.008665 amuElectron(-1)0.000548 amuNuclear Energy (Basics: Atomic Structure)Positron (e+, b+) Positively charged electron

Neutrino (u) Electrically neutral. Do not react.*

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Fission Chain Reaction

*Fission Chain ReactionIn the fission reaction the incident neutron enters the heavy target nucleus, forming a compound nucleus that is excited to such a high energy level that the nucleus "splits (fissions) into two large fragments plus some neutrons

A large amount of energy is released in the form of radiation and fragment kinetic energy

*Neutrons and Chain ReactionReactor Core components such as: Fuel, Moderator, Control rod, Coolant, Shielding material have negative contribution in neutron populationOnly contribution to neutron population is from nuclear fuel i.e., U-235 or U-238 (Small contribution)

Nuclear Energy (Nuclear Equations)In balancing nuclear eqns., the same nucleons show up in the products as entered the reaction. e.g.To balance, the following relationship must be satisfied:Sometimes the symbols or are added to products to indicate emission of electromagnetic radiation or a neutrino. They have no effect on balancing as both have zero Z and A.

Reactions are either exothermic or endothermic.*

235U + n 236U* (A1,Z1) + (A2,Z2) + Nn + E Z1 + Z2 = 92, A1 + A2 + N = 236 A1 = A2, symmetric fission rare (~0.01%) Capture of neutron by 235U forms compound nucleus(*) ~2.4 (on average) prompt neutrons released per fission event Immediate products are called fission fragments. They, and their decayed products, are called fission products.

Nuclear Energy (Basics: Fission Equation)235U + 1n 236U* 137Ba + 97Kr + 2 1n + E 92 0 92 5636 0*

Symmetric FissionNuclear Energy (Basics: Fission Yield)75 A 160The probability that aparticular pair offission fragments willbe produced by fissionMost probable fission productranges:

and85 A 105130 A 150*

*Mass Defect (Cont.)The mass defect can be calculated using Equation:

*Mass Defect (Cont.)

*Mass Defect (Cont.)

Where is the remaining mass?

*The answer lies in energy-mass equivalence formula (E = mc2) and total energy balance Starting with the compound nucleus, energy is required to break all the liaisons between nucleons and finally obtain separate nucleons ORThe amount of energy that would be released if the nucleus was formed from the separate particlesThis energy is called the binding energy and is equivalent to the mass defectBinding Energy

*Of course the heavier is the nucleus, the larger is the overall binding energy, and this is why we usually consider the binding energy divided by the number of nucleons to get a unitary binding energy allowing to compare the stability of different nuclei Binding Energy (Cont.)

*Binding Energy (Cont.)The variation of the binding energy with mass number

*Binding Energy (Cont.)The figure is based on experimental resultsFrom the figure it is clear that: Binding energy per nucleon in nuclei grows to about A = 60 (except in the case of some light nuclei) and Binding energy then gradually decreases; i.e., the middle nuclei are more strongly bound than the light or heavy nuclei Binding energy can be released either from light nuclei by fusion or from heavy nuclei by fission When light elements fuse into larger groups, they lose mass, and heavy nuclei lose mass when they divide

*

Cross Sections

*Cross SectionsThe probability of occurrence of a particular reaction between a neutron and a nucleus is called microscopic cross section ( ) of the nucleusThis cross section varies with neutron energy represents the effective target area that a single nucleus presents to a bombarding particle The larger the effective area, the greater the probability for reactionThe units are given in barns or cm2 (1 barn = 10-24 cm2)

*Cross Sections (Cont.)Macroscopic cross section () is the probability of a given reaction occurring per unit travel of the neutron is related to the by the relationship: = N represents the effective target area that is presented by all of the nuclei (N) contained in one cm3 of the material The units are given as 1/cm or cm-1

The product sN is equal to the total cross-section of all the nuclei present in a unit volume and is called macroscopic cross-section () and has units cm2/cm3 or cm-1. It can also be explained as the probability per unit length that a neutron will collide, i.e. the collision cross-section. Macroscopic cross-sections are also designated according to the reaction they represent. etc. = 1/ = mean free path. Represents the average distance that a neutron travels without making a collision or interaction with a target nucleus.For an element of atomic mass (A) and density r (g/cm3), N (nuclei/cm3) can be calculated fromNuclear Energy (Cross-section)*

Neutron Moderation

*Neutron ModerationThe process of reducing the energy of a neutron to the thermal region by elastic scattering is referred to as thermalization, slowing down, or moderation. The material used for the purpose of thermalizing neutrons is called a moderator.The fast neutrons are slowed down by making them lose their energy to the nuclei of some light element by undergoing successive collisions

*Neutron Moderation (Cont.)Moderating materials should be of Low mass numberHigh scattering cross-sectionLow absorption cross-sectionAdditional properties may includeHigh thermal conductivityChemically stable with respect to fuel and claddingStable against irradiationStable against temperature variation

Reactor Power

*Reaction RatesThe reaction rate (R) is the product of macroscopic cross section and the total path length of all the neutrons in a cubic centimeter in a second (neutron flux )R = where:R = reaction rate (reactions/sec) = neutron flux (neutrons/cm2-sec) = macroscopic cross section (cm-1)

*Reactor PowerReactor power is the energy release by fission in a reactor in unit timeTotal fission per second will be the reaction rate multiplied by the reactor volume P = R V = V

MASS OF REACTANTS U: 235.0439 amu n: 1.00867 amu

--------------------------------Total : 236.05257 amu --------------------------------MASS OF PRODUCTS Ba: 136.9061 amu Kr: 96.9212 amu 2 n: 2(1.00867) amu--------------------------------Total: 235.84464 amu--------------------------------Dm = 235.84464 - 236.05257 = -0.20793 amu = -193.583 MeVNuclear Energy (Energy Released)For the reaction,235U + 1n 137Ba + 97Kr + 2 1n920 56 36 0which is the same for U-233 and Pu-239.More energy is, however released due to (i) slow decay of the fission fragments, and (ii) non-fission capture of excess neutrons in reactions that produce energy, though much less than that of fission.*

The total energy produced per fission reaction is about 200 MeV.The complete fission of 1g of U-235 nuclei thus produces,Nuclear Energy (Energy Released)Avagadros Number x 200 MeV = 0.60225x1024 x 200 U-235 mass235.0439= 0.513x1024 MeV= 2.276x1024 kWh= 8.19x1010 J= 0.948 MW-day

Fuel burnup: The amount of energy in MW-days produced of each metric ton of fuel.Fuel: All uranium, plutonium and thorium isotopes. Does not include other compounds or mixtures. Fuel material refers to fuel plus such other material.*

The total energy from fission after all of the particles from decay have been released, is about 200 MeV.Nuclear Energy (Basics: Energy from Fission)*

MeVFission fragment kinetic energy166Neutrons5Prompt gamma rays7Fission product gamma rays7Beta particles5Neutrinos10Total200

*Reactor Power1 MeV = 1.60217646 10-13 joules1 fission releases 200 MeV = 3.2 10-11 joulesEnergy release per fission = 3.2 10-11 joulesEnergy release per fission = 1/(3.12 1010) joulesPower = energy release per unit time (J/s = watts)Power per fission = 1/(3.12 1010) wattsTherefore, reactor power will be:P = total fission per second * power per fissionP = V * 1/(3.12 1010) (watts)

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Reactivity

*ReactivityReactivity () is a measure of the departure of a reactor from criticality. The reactivity is related to the value of keffReactivity is a useful concept to predict how the neutron population of a reactor will change over time. may be positive, zero, or negative, depending upon the value of keff.Reactivity of a critical reactor is zero.

*Reactivity (Cont.)No =neutrons in the preceding generationNo(keff)=neutrons in the present generation (Nokeff - No)=numerical change in neutron PopulationFractional change in present generation is

This fractional change in neutron population per generation is referred to as reactivity ().

*Reactivity (Cont.)Units A dimensionless number A ratio of two dimensionless quantitiesArtificial units are defined.k/k % k/k and pcm (percent millirho)

*Modes of Radioactive DecayNuclides heavier than Pb (Z=82), and a few light nuclei are unstable To form stable nuclei these undergo radioactive decay by emitting radiation - particles (-ve charge 1)- particles (+ve charge 2)

*RadioactivityRadioactivity is the property of certain nuclides of spontaneously emitting particles or gammaradiation

*Radioactivity (Cont.)The activity (A) is the number of atoms that disintegrate in unit time The unit of activity number of disintegrations per second OR BqCi (3.7*1010 Bq)

*Radioactivity (Cont.)Half-life is defined as the time necessary for a significant number of atoms to reduce to half, and is represented by tA = Ao e-tA/Ao = e-t ln (A/Ao) = -tt = - ln (A/Ao)/ At t = t - A = Ao/2t = -ln(1/2)/ = ln2/ = 0.693/

Thank you *

**Why does this equation give us usable energy? Because of binding energy. When neutrons and protons come together to form an element, the sum total of their individual masses is more than the mass of the element. Where does this mass go? It is converted into binding energy and it is the energy that holds the atom together. The amount may be determined by the following equation-E= mc2

Familiar? Well, the binding energy curve tells us that the energy per nuclear constituent goes down on either side of iron. If I can split an atom into two smaller atoms that have higher binding energy, then there should be some mass left over- i.e., some energy. To illustrate, look at the above reaction.*Course participants should be able to recognise the higher risk in use of that portable gamma radiography equipment.

The higher risk are associated with the field use of the equipment where public access may be possible, the design which often involves the source leaving a shielded position and the high reliance of operator following safe procedures.*Course participants should be able to recognise the higher risk in use of that portable gamma radiography equipment.

The higher risk are associated with the field use of the equipment where public access may be possible, the design which often involves the source leaving a shielded position and the high reliance of operator following safe procedures.*Course participants should be able to recognise the higher risk in use of that portable gamma radiography equipment.

The higher risk are associated with the field use of the equipment where public access may be possible, the design which often involves the source leaving a shielded position and the high reliance of operator following safe procedures.*

Confusing? Discuss.

How is the energy released? Primarily in the form of kinetic energy for the fission fragments and the neutrons. But some is released in the form of gamma rays or other high energy photons.

So, how do things get hot? Well, these fast moving particles are bound to hit other things. This causes a transfer of energy to the material lattice and everything starts to vibrate- increase in internal kinetic energy- temperature rises. Eventually, everything gets real hot.

*Nightmare slide

Confusing? Discuss.

How is the energy released? Primarily in the form of kinetic energy for the fission fragments and the neutrons. But some is released in the form of gamma rays or other high energy photons.

So, how do things get hot? Well, these fast moving particles are bound to hit other things. This causes a transfer of energy to the material lattice and everything starts to vibrate- increase in internal kinetic energy- temperature rises. Eventually, everything gets real hot.